Geodesic
On critical exponents in fixed points of k-uniform binary morphisms
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 41-68.

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Let 𝐰 be an infinite fixed point of a binary k-uniform morphism f, and let E(𝐰) be the critical exponent of 𝐰. We give necessary and sufficient conditions for E(𝐰) to be bounded, and an explicit formula to compute it when it is. In particular, we show that E(𝐰) is always rational. We also sketch an extension of our method to non-uniform morphisms over general alphabets.

DOI : 10.1051/ita:2007042
Classification : 68R15
Mots-clés : critical exponent, binary k-uniform morphism 
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     title = {On critical exponents in fixed points of $k$-uniform binary morphisms},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {41--68},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {1},
     year = {2009},
     doi = {10.1051/ita:2007042},
     zbl = {1170.68034},
     mrnumber = {2483444},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007042/}
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Krieger, Dalia. On critical exponents in fixed points of $k$-uniform binary morphisms. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 41-68. doi : 10.1051/ita:2007042. https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007042/

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